Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1938 conjugacy classes of subgroups.
The subgroup lattice has 523 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61376 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #61089 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #60626 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #33248 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #33064 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #28763 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #28734 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #27809 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #27292 | C2 | 1 | 8 | yes | maximal, complemented |
| 10 | #25928 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #25878 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #22466 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #21661 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #20514 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×#576 | C22 | 1 | 2 | yes | — |
| 16 | #3504 | C22 | 1 | 2 | yes | complemented |
| 17 | #3498 | C22 | 1 | 2 | yes | — |
| 18 | #3388 | — | 2 | 4 | no | — |
| 19 | #3383 | — | 2 | 2 | no | — |
| 20 | #3380 | — | 2 | 2 | no | — |
| 21 | #3287 | — | 2 | 2 | no | — |
| 22 | D4×D8 | — | 2 | 2 | no | — |
| 23 | #3274 | — | 2 | 4 | no | — |
| 24 | #3164 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×#499 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×#493 | C22 | 1 | 1 | yes | characteristic |
| 27 | #3142 | — | 2 | 2 | no | — |
| 28 | #3142 | C22 | 1 | 2 | yes | — |
| 29 | #3138 | — | 2 | 2 | no | — |
| 30 | #3138 | C22 | 1 | 2 | yes | complemented |
| 31 | #3136 | — | 2 | 8 | no | — |
| 32 | #3136 | C22 | 1 | 8 | yes | complemented |
| 33 | #3135 | — | 2 | 2 | no | — |
| 34 | #3135 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#490 | — | 2 | 2 | no | — |
| 36 | C2×#490 | C22 | 1 | 2 | yes | complemented |
| 37 | #3084 | C22 | 1 | 4 | yes | complemented |
| 38 | #3080 | C22 | 1 | 2 | yes | complemented |
| 39 | #3058 | C22 | 1 | 2 | yes | — |
| 40 | #3038 | C22 | 1 | 2 | yes | — |
| 41 | #3008 | C22 | 1 | 4 | yes | — |
| 42 | #2960 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×#443 | C22 | 1 | 2 | yes | — |
| 44 | #2951 | C22 | 1 | 2 | yes | — |
| 45 | C4×#135 | C22 | 1 | 1 | yes | characteristic |
| 46 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 47 | #2897 | C22 | 1 | 8 | yes | complemented |
| 48 | #2875 | C22 | 1 | 2 | yes | complemented |
| 49 | #2641 | C22 | 1 | 2 | yes | complemented |
| 50 | #2079 | C22 | 1 | 4 | yes | complemented |
| 51 | #2045 | C22 | 1 | 4 | yes | complemented |
| 52 | #2037 | C22 | 1 | 8 | yes | complemented |
| 53 | #2027 | C22 | 1 | 8 | yes | complemented |
| 54 | #1998 | C22 | 1 | 2 | yes | complemented |
| 55 | #1995 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | #1978 | C22 | 1 | 4 | yes | complemented |
| 57 | #1972 | C22 | 1 | 4 | yes | complemented |
| 58 | #1970 | C22 | 1 | 4 | yes | complemented |
| 59 | #1965 | C22 | 1 | 2 | yes | complemented |
| 60 | #1963 | C22 | 1 | 1 | yes | characteristic |
| 61 | #1938 | C22 | 1 | 4 | yes | complemented |
| 62 | #1931 | C22 | 1 | 8 | yes | complemented |
| 63 | #1907 | C22 | 1 | 8 | yes | complemented |
| 64 | #1883 | C22 | 1 | 8 | yes | complemented |
| 65 | #1838 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | #1816 | C22 | 1 | 4 | yes | complemented |
| 67 | #1792 | C22 | 1 | 8 | yes | complemented |
| 68 | C4×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | #1772 | C22 | 1 | 2 | yes | complemented |
| 70 | #1765 | C22 | 1 | 4 | yes | complemented |
| 71 | #1764 | C22 | 1 | 4 | yes | complemented |
| 72 | #1759 | C22 | 1 | 2 | yes | complemented |
| 73 | #1726 | C22 | 1 | 1 | yes | characteristic, complemented |
| 74 | C2×H(5,𝔽2) | C23 | 1 | 4 | yes | — |
| 75 | #576 | — | 2 | 16 | no | — |
| 76 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 77 | C2×AGL(1,ℤ/8) | C23 | 1 | 4 | yes | — |
| 78 | C2×#135 | — | 2 | 2 | no | — |
| 79 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×D8 | — | 2 | 2 | no | — |
| 81 | C22×D8 | C23 | 1 | 2 | yes | — |
| 82 | C22×D8 | C23 | 1 | 2 | yes | — |
| 83 | C2×#131 | C23 | 1 | 2 | yes | — |
| 84 | C2×#131 | C23 | 1 | 4 | yes | — |
| 85 | #557 | — | 2 | 4 | no | — |
| 86 | #554 | — | 2 | 4 | no | — |
| 87 | #554 | — | 4 | 4 | no | — |
| 88 | #550 | — | 2 | 4 | no | — |
| 89 | D42 | — | 2 | 4 | no | — |
| 90 | D42 | — | 4 | 4 | no | — |
| 91 | #544 | — | 2 | 4 | no | — |
| 92 | #544 | C23 | 1 | 4 | yes | — |
| 93 | #535 | — | 2 | 4 | no | — |
| 94 | #535 | C23 | 1 | 4 | yes | — |
| 95 | #533 | — | 2 | 2 | no | — |
| 96 | #533 | C23 | 1 | 1 | yes | characteristic |
| 97 | #532 | — | 2 | 2 | no | — |
| 98 | #532 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×#127 | — | 2 | 2 | no | — |
| 100 | C2×#127 | C23 | 1 | 2 | yes | — |
| 101 | C2×#125 | — | 2 | 2 | no | — |
| 102 | C2×#125 | C23 | 1 | 2 | yes | — |
| 103 | #520 | C23 | 1 | 4 | yes | — |
| 104 | C4×#41 | C23 | 1 | 2 | yes | — |
| 105 | #501 | — | 2 | 4 | no | — |
| 106 | #500 | — | 2 | 2 | no | — |
| 107 | #499 | — | 2 | 2 | no | — |
| 108 | #499 | — | 2 | 2 | no | — |
| 109 | #499 | — | 2 | 2 | no | — |
| 110 | #493 | — | 2 | 2 | no | — |
| 111 | #493 | — | 2 | 2 | no | — |
| 112 | #491 | — | 2 | 2 | no | — |
| 113 | #491 | D4 | 1 | 1 | yes | characteristic |
| 114 | #491 | D4 | 1 | 1 | yes | characteristic |
| 115 | #490 | — | 2 | 2 | no | — |
| 116 | #490 | — | 2 | 2 | no | — |
| 117 | #490 | — | 2 | 2 | no | — |
| 118 | #490 | — | 2 | 8 | no | — |
| 119 | #490 | — | 2 | 2 | no | — |
| 120 | #490 | — | 2 | 4 | no | — |
| 121 | #490 | — | 2 | 2 | no | — |
| 122 | #490 | D4 | 1 | 1 | yes | characteristic |
| 123 | #490 | D4 | 1 | 1 | yes | characteristic |
| 124 | #489 | — | 2 | 8 | no | — |
| 125 | #489 | D4 | 1 | 4 | yes | — |
| 126 | #488 | — | 2 | 4 | no | — |
| 127 | #488 | — | 2 | 8 | no | — |
| 128 | #486 | — | 2 | 4 | no | — |
| 129 | #486 | — | 2 | 8 | no | — |
| 130 | #479 | — | 2 | 4 | no | — |
| 131 | #479 | — | 2 | 4 | no | — |
| 132 | #478 | — | 2 | 4 | no | — |
| 133 | #478 | — | 2 | 4 | no | — |
| 134 | #476 | — | 2 | 4 | no | — |
| 135 | #475 | — | 2 | 4 | no | — |
| 136 | #469 | — | 2 | 4 | no | — |
| 137 | #466 | — | 2 | 4 | no | — |
| 138 | #460 | — | 2 | 4 | no | — |
| 139 | #459 | — | 2 | 4 | no | — |
| 140 | #449 | — | 2 | 8 | no | — |
| 141 | #447 | — | 2 | 8 | no | — |
| 142 | #446 | — | 2 | 2 | no | — |
| 143 | C8×Q8 | — | 2 | 2 | no | — |
| 144 | #443 | — | 2 | 8 | no | — |
| 145 | #440 | — | 2 | 4 | no | — |
| 146 | C4×Q16 | — | 2 | 2 | no | — |
| 147 | C4×Q16 | D4 | 1 | 2 | yes | — |
| 148 | C4×SD16 | D4 | 1 | 4 | yes | — |
| 149 | C4×D8 | — | 2 | 2 | no | — |
| 150 | C4×D8 | D4 | 1 | 2 | yes | — |
| 151 | #436 | — | 2 | 2 | no | — |
| 152 | C8×D4 | — | 2 | 2 | no | — |
| 153 | C2×#108 | C23 | 1 | 2 | yes | — |
| 154 | #428 | C23 | 1 | 4 | yes | — |
| 155 | #427 | C23 | 1 | 1 | yes | characteristic |
| 156 | C2×#107 | C23 | 1 | 2 | yes | — |
| 157 | C2×#106 | C23 | 1 | 2 | yes | — |
| 158 | #424 | C23 | 1 | 2 | yes | — |
| 159 | #423 | C23 | 1 | 1 | yes | characteristic |
| 160 | #423 | C23 | 1 | 1 | yes | characteristic |
| 161 | C2×#104 | C23 | 1 | 4 | yes | — |
| 162 | C2×#104 | C23 | 1 | 4 | yes | — |
| 163 | #418 | — | 2 | 8 | no | — |
| 164 | #418 | C23 | 1 | 8 | yes | — |
| 165 | #418 | C23 | 1 | 4 | yes | — |
| 166 | #417 | — | 2 | 8 | no | — |
| 167 | #417 | C23 | 1 | 4 | yes | — |
| 168 | #417 | C23 | 1 | 8 | yes | — |
| 169 | #416 | — | 2 | 8 | no | — |
| 170 | #416 | C23 | 1 | 2 | yes | — |
| 171 | #416 | C23 | 1 | 4 | yes | — |
| 172 | C2×#102 | — | 2 | 8 | no | — |
| 173 | C2×#102 | C23 | 1 | 8 | yes | — |
| 174 | C2×#100 | C23 | 1 | 8 | yes | — |
| 175 | #408 | C23 | 1 | 2 | yes | — |
| 176 | #405 | — | 2 | 4 | no | — |
| 177 | #405 | C23 | 1 | 4 | yes | — |
| 178 | #405 | C23 | 1 | 2 | yes | — |
| 179 | C4×M16 | — | 2 | 2 | no | — |
| 180 | C4×M16 | C23 | 1 | 2 | yes | — |
| 181 | C2×#97 | — | 2 | 2 | no | — |
| 182 | C2×#97 | C23 | 1 | 2 | yes | — |
| 183 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 184 | C2×C4×C8 | C23 | 1 | 2 | yes | — |
| 185 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 186 | #394 | — | 4 | 4 | no | — |
| 187 | #390 | C23 | 1 | 8 | yes | — |
| 188 | #376 | C23 | 1 | 1 | yes | characteristic |
| 189 | #343 | C23 | 1 | 8 | yes | — |
| 190 | #341 | C23 | 1 | 2 | yes | — |
| 191 | #341 | C23 | 1 | 4 | yes | — |
| 192 | #339 | C23 | 1 | 4 | yes | — |
| 193 | #339 | C23 | 1 | 4 | yes | — |
| 194 | H(5,𝔽2) | — | 2 | 16 | no | — |
| 195 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 196 | C2×#41 | — | 2 | 4 | no | — |
| 197 | C2×#41 | — | 2 | 4 | no | — |
| 198 | C2×#41 | C24 | 1 | 2 | yes | — |
| 199 | C2×#41 | C24 | 1 | 2 | yes | — |
| 200 | C22×D4 | — | 2 | 4 | no | — |
| 201 | C22×D4 | — | 2 | 4 | no | — |
| 202 | C22×D4 | — | 2 | 4 | no | — |
| 203 | C22×D4 | — | 4 | 4 | no | — |
| 204 | C22×D4 | — | 4 | 4 | no | — |
| 205 | C22×D4 | C24 | 1 | 4 | yes | — |
| 206 | AGL(1,ℤ/8) | — | 2 | 16 | no | — |
| 207 | AGL(1,ℤ/8) | — | 4 | 16 | no | — |
| 208 | #135 | — | 4 | 8 | no | — |
| 209 | #135 | #41 | 1 | 8 | yes | — |
| 210 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C2×SD16 | — | 2 | 4 | no | — |
| 212 | C2×SD16 | C2×D4 | 1 | 2 | yes | — |
| 213 | C2×D8 | — | 2 | 4 | no | — |
| 214 | C2×D8 | — | 2 | 2 | no | — |
| 215 | C2×D8 | — | 2 | 2 | no | — |
| 216 | C2×D8 | — | 2 | 4 | no | — |
| 217 | C2×D8 | — | 2 | 8 | no | — |
| 218 | C2×D8 | — | 4 | 4 | no | — |
| 219 | C2×D8 | — | 4 | 8 | no | — |
| 220 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | #131 | — | 2 | 8 | no | — |
| 222 | #131 | — | 2 | 8 | no | — |
| 223 | #131 | — | 4 | 4 | no | — |
| 224 | C2×M16 | — | 2 | 2 | no | — |
| 225 | C2×M16 | — | 2 | 4 | no | — |
| 226 | C2×M16 | C24 | 1 | 2 | yes | — |
| 227 | C2×M16 | C24 | 1 | 4 | yes | — |
| 228 | C2×M16 | C24 | 1 | 2 | yes | — |
| 229 | C22×C8 | — | 2 | 2 | no | — |
| 230 | C22×C8 | — | 2 | 4 | no | — |
| 231 | C22×C8 | C24 | 1 | 2 | yes | — |
| 232 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 233 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 234 | C4⋊Q8 | — | 2 | 4 | no | — |
| 235 | C4⋊Q8 | — | 2 | 4 | no | — |
| 236 | C4⋊Q8 | — | 4 | 4 | no | — |
| 237 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 239 | #127 | — | 2 | 4 | no | — |
| 240 | #127 | — | 2 | 2 | no | — |
| 241 | #127 | — | 2 | 2 | no | — |
| 242 | #127 | — | 2 | 4 | no | — |
| 243 | #127 | — | 4 | 4 | no | — |
| 244 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 245 | #125 | — | 2 | 4 | no | — |
| 246 | #125 | — | 2 | 4 | no | — |
| 247 | #125 | — | 2 | 2 | no | — |
| 248 | #125 | — | 2 | 2 | no | — |
| 249 | #125 | — | 2 | 4 | no | — |
| 250 | #125 | — | 4 | 4 | no | — |
| 251 | #125 | — | 4 | 4 | no | — |
| 252 | #125 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | #125 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | #124 | — | 2 | 4 | no | — |
| 255 | #124 | C2×D4 | 1 | 2 | yes | — |
| 256 | C22⋊Q8 | — | 2 | 2 | no | — |
| 257 | C22⋊Q8 | — | 4 | 4 | no | — |
| 258 | C22⋊Q8 | — | 4 | 4 | no | — |
| 259 | C22⋊Q8 | — | 4 | 4 | no | — |
| 260 | C22⋊Q8 | — | 4 | 4 | no | — |
| 261 | #121 | — | 2 | 2 | no | — |
| 262 | #121 | — | 2 | 8 | no | — |
| 263 | #121 | — | 4 | 8 | no | — |
| 264 | #121 | — | 4 | 4 | no | — |
| 265 | #120 | — | 4 | 8 | no | — |
| 266 | #120 | — | 4 | 4 | no | — |
| 267 | C4×Q8 | — | 2 | 2 | no | — |
| 268 | C4×Q8 | — | 2 | 4 | no | — |
| 269 | C4×Q8 | — | 4 | 4 | no | — |
| 270 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 271 | C4×D4 | — | 2 | 4 | no | — |
| 272 | C4×D4 | — | 2 | 4 | no | — |
| 273 | C4×D4 | — | 2 | 2 | no | — |
| 274 | C4×D4 | — | 4 | 4 | no | — |
| 275 | C4×D4 | — | 4 | 4 | no | — |
| 276 | C4×D4 | C2×D4 | 1 | 4 | yes | — |
| 277 | #117 | — | 2 | 2 | no | — |
| 278 | #117 | — | 2 | 4 | no | — |
| 279 | #117 | C24 | 1 | 2 | yes | — |
| 280 | #117 | C24 | 1 | 2 | yes | — |
| 281 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 282 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 283 | C2×C4⋊C4 | — | 4 | 4 | no | — |
| 284 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 285 | C2×C22⋊C4 | — | 4 | 8 | no | — |
| 286 | C2×C42 | — | 2 | 2 | no | — |
| 287 | C2×C42 | C24 | 1 | 2 | yes | — |
| 288 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 289 | #108 | — | 2 | 4 | no | — |
| 290 | #107 | — | 2 | 2 | no | — |
| 291 | #107 | — | 2 | 2 | no | — |
| 292 | #107 | — | 2 | 4 | no | — |
| 293 | #107 | C2×D4 | 1 | 2 | yes | — |
| 294 | #106 | — | 2 | 4 | no | — |
| 295 | #106 | — | 2 | 4 | no | — |
| 296 | #106 | C2×D4 | 1 | 2 | yes | — |
| 297 | C4⋊C8 | — | 2 | 2 | no | — |
| 298 | C4⋊C8 | — | 2 | 2 | no | — |
| 299 | C4⋊C8 | — | 2 | 2 | no | — |
| 300 | C4⋊C8 | — | 2 | 2 | no | — |
| 301 | #104 | — | 2 | 8 | no | — |
| 302 | #104 | — | 4 | 4 | no | — |
| 303 | #103 | — | 2 | 8 | no | — |
| 304 | #103 | — | 2 | 4 | no | — |
| 305 | #103 | C2×D4 | 1 | 4 | yes | — |
| 306 | #103 | C2×D4 | 1 | 4 | yes | — |
| 307 | #103 | C2×D4 | 1 | 4 | yes | — |
| 308 | #102 | — | 2 | 8 | no | — |
| 309 | #102 | — | 2 | 4 | no | — |
| 310 | #102 | — | 2 | 8 | no | — |
| 311 | #102 | — | 2 | 8 | no | — |
| 312 | #102 | — | 2 | 8 | no | — |
| 313 | #102 | — | 2 | 8 | no | — |
| 314 | #102 | — | 2 | 8 | no | — |
| 315 | #102 | C2×D4 | 1 | 4 | yes | — |
| 316 | #102 | C2×D4 | 1 | 4 | yes | — |
| 317 | #102 | C2×D4 | 1 | 4 | yes | — |
| 318 | #100 | — | 4 | 8 | no | — |
| 319 | C22⋊C8 | — | 2 | 4 | no | — |
| 320 | #97 | — | 2 | 4 | no | — |
| 321 | #97 | — | 2 | 2 | no | — |
| 322 | #97 | — | 2 | 2 | no | — |
| 323 | #97 | — | 4 | 2 | no | — |
| 324 | #97 | C2×D4 | 1 | 1 | yes | characteristic |
| 325 | #97 | C2×D4 | 1 | 1 | yes | characteristic |
| 326 | #97 | C2×D4 | 1 | 2 | yes | — |
| 327 | C4×C8 | — | 2 | 4 | no | — |
| 328 | C4×C8 | — | 2 | 2 | no | — |
| 329 | C4×C8 | — | 2 | 4 | no | — |
| 330 | C4×C8 | — | 2 | 2 | no | — |
| 331 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 332 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 333 | #95 | — | 2 | 2 | no | — |
| 334 | C24 | — | 2 | 4 | no | — |
| 335 | C24 | — | 4 | 4 | no | — |
| 336 | #41 | — | 2 | 4 | no | — |
| 337 | #41 | — | 2 | 4 | no | — |
| 338 | #41 | — | 2 | 4 | no | — |
| 339 | #41 | — | 4 | 16 | no | — |
| 340 | #41 | — | 4 | 8 | no | — |
| 341 | #41 | — | 8 | 4 | no | — |
| 342 | #41 | C2×#41 | 1 | 8 | yes | — |
| 343 | C2×Q8 | — | 2 | 2 | no | — |
| 344 | C2×Q8 | — | 4 | 4 | no | — |
| 345 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 346 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 347 | C2×D4 | — | 2 | 2 | no | — |
| 348 | C2×D4 | — | 2 | 2 | no | — |
| 349 | C2×D4 | — | 2 | 2 | no | — |
| 350 | C2×D4 | — | 2 | 4 | no | — |
| 351 | C2×D4 | — | 2 | 4 | no | — |
| 352 | C2×D4 | — | 2 | 8 | no | — |
| 353 | C2×D4 | — | 2 | 8 | no | — |
| 354 | C2×D4 | — | 4 | 16 | no | — |
| 355 | C2×D4 | — | 4 | 4 | no | — |
| 356 | C2×D4 | — | 4 | 4 | no | — |
| 357 | C2×D4 | — | 4 | 8 | no | — |
| 358 | C2×D4 | — | 4 | 8 | no | — |
| 359 | C2×D4 | — | 4 | 4 | no | — |
| 360 | C2×D4 | — | 4 | 4 | no | — |
| 361 | C2×D4 | — | 8 | 4 | no | — |
| 362 | C2×D4 | — | 8 | 16 | no | — |
| 363 | C2×D4 | — | 16 | 4 | no | — |
| 364 | C2×D4 | — | 16 | 8 | no | — |
| 365 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 366 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 367 | C22×C4 | — | 2 | 2 | no | — |
| 368 | C22×C4 | — | 2 | 2 | no | — |
| 369 | C22×C4 | — | 2 | 4 | no | — |
| 370 | C22×C4 | — | 2 | 2 | no | — |
| 371 | C22×C4 | — | 2 | 4 | no | — |
| 372 | C22×C4 | — | 4 | 4 | no | — |
| 373 | C22×C4 | — | 4 | 4 | no | — |
| 374 | C22×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 375 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 376 | Q16 | #124 | 1 | 4 | yes | — |
| 377 | SD16 | — | 4 | 8 | no | — |
| 378 | SD16 | #124 | 1 | 8 | yes | — |
| 379 | D8 | — | 4 | 8 | no | — |
| 380 | D8 | — | 4 | 4 | no | — |
| 381 | D8 | — | 4 | 4 | no | — |
| 382 | D8 | — | 8 | 4 | no | — |
| 383 | D8 | #124 | 1 | 4 | yes | — |
| 384 | M16 | — | 2 | 4 | no | — |
| 385 | M16 | — | 2 | 4 | no | — |
| 386 | M16 | — | 2 | 4 | no | — |
| 387 | M16 | — | 2 | 4 | no | — |
| 388 | M16 | — | 4 | 8 | no | — |
| 389 | M16 | — | 4 | 4 | no | — |
| 390 | C2×C8 | — | 2 | 2 | no | — |
| 391 | C2×C8 | — | 2 | 2 | no | — |
| 392 | C2×C8 | — | 2 | 2 | no | — |
| 393 | C2×C8 | — | 2 | 4 | no | — |
| 394 | C2×C8 | — | 2 | 2 | no | — |
| 395 | C2×C8 | — | 2 | 2 | no | — |
| 396 | C2×C8 | — | 4 | 8 | no | — |
| 397 | C2×C8 | — | 4 | 4 | no | — |
| 398 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 399 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 400 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 401 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 402 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 403 | C2×C8 | C2×#41 | 1 | 4 | yes | — |
| 404 | C4⋊C4 | — | 2 | 2 | no | — |
| 405 | C4⋊C4 | — | 2 | 4 | no | — |
| 406 | C4⋊C4 | — | 2 | 2 | no | — |
| 407 | C4⋊C4 | — | 2 | 2 | no | — |
| 408 | C4⋊C4 | — | 2 | 2 | no | — |
| 409 | C4⋊C4 | — | 2 | 4 | no | — |
| 410 | C4⋊C4 | — | 2 | 4 | no | — |
| 411 | C4⋊C4 | — | 4 | 4 | no | — |
| 412 | C4⋊C4 | — | 4 | 4 | no | — |
| 413 | C4⋊C4 | — | 4 | 4 | no | — |
| 414 | C4⋊C4 | — | 4 | 4 | no | — |
| 415 | C4⋊C4 | — | 4 | 4 | no | — |
| 416 | C4⋊C4 | — | 4 | 4 | no | — |
| 417 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 418 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 419 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 420 | C22⋊C4 | — | 2 | 2 | no | — |
| 421 | C22⋊C4 | — | 2 | 2 | no | — |
| 422 | C22⋊C4 | — | 2 | 4 | no | — |
| 423 | C22⋊C4 | — | 2 | 4 | no | — |
| 424 | C22⋊C4 | — | 4 | 8 | no | — |
| 425 | C22⋊C4 | — | 4 | 4 | no | — |
| 426 | C22⋊C4 | — | 16 | 8 | no | — |
| 427 | C42 | — | 2 | 4 | no | — |
| 428 | C42 | — | 2 | 2 | no | — |
| 429 | C42 | — | 2 | 2 | no | — |
| 430 | C42 | — | 2 | 2 | no | — |
| 431 | C42 | — | 2 | 2 | no | — |
| 432 | C42 | — | 4 | 4 | no | — |
| 433 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 434 | C42 | C22×D4 | 1 | 2 | yes | — |
| 435 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 436 | C23 | — | 2 | 2 | no | — |
| 437 | C23 | — | 2 | 2 | no | — |
| 438 | C23 | — | 4 | 4 | no | — |
| 439 | C23 | — | 4 | 8 | no | — |
| 440 | C23 | — | 8 | 8 | no | — |
| 441 | C23 | — | 8 | 8 | no | — |
| 442 | C23 | — | 16 | 8 | no | — |
| 443 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 444 | Q8 | — | 2 | 2 | no | — |
| 445 | Q8 | — | 2 | 4 | no | — |
| 446 | Q8 | — | 8 | 2 | no | — |
| 447 | Q8 | — | 16 | 4 | no | — |
| 448 | Q8 | C2×#124 | 1 | 4 | yes | — |
| 449 | D4 | — | 2 | 8 | no | — |
| 450 | D4 | — | 2 | 4 | no | — |
| 451 | D4 | — | 2 | 2 | no | — |
| 452 | D4 | — | 4 | 4 | no | — |
| 453 | D4 | — | 4 | 4 | no | — |
| 454 | D4 | — | 4 | 4 | no | — |
| 455 | D4 | — | 4 | 8 | no | — |
| 456 | D4 | — | 4 | 4 | no | — |
| 457 | D4 | — | 8 | 8 | no | — |
| 458 | D4 | — | 8 | 8 | no | — |
| 459 | D4 | — | 8 | 8 | no | — |
| 460 | D4 | — | 16 | 4 | no | — |
| 461 | D4 | — | 16 | 8 | no | — |
| 462 | D4 | C2×#124 | 1 | 4 | yes | — |
| 463 | C2×C4 | — | 2 | 2 | no | — |
| 464 | C2×C4 | — | 2 | 8 | no | — |
| 465 | C2×C4 | — | 2 | 4 | no | — |
| 466 | C2×C4 | — | 2 | 2 | no | — |
| 467 | C2×C4 | — | 2 | 2 | no | — |
| 468 | C2×C4 | — | 2 | 2 | no | — |
| 469 | C2×C4 | — | 4 | 2 | no | — |
| 470 | C2×C4 | — | 4 | 2 | no | — |
| 471 | C2×C4 | — | 4 | 2 | no | — |
| 472 | C2×C4 | — | 4 | 4 | no | — |
| 473 | C2×C4 | — | 4 | 4 | no | — |
| 474 | C2×C4 | — | 4 | 2 | no | — |
| 475 | C2×C4 | — | 8 | 4 | no | — |
| 476 | C2×C4 | — | 8 | 8 | no | — |
| 477 | C2×C4 | — | 8 | 4 | no | — |
| 478 | C2×C4 | — | 16 | 4 | no | — |
| 479 | C2×C4 | D42 | 1 | 2 | yes | — |
| 480 | C2×C4 | D42 | 1 | 2 | yes | — |
| 481 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 482 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 483 | C2×C4 | C22×#41 | 1 | 2 | yes | — |
| 484 | C2×C4 | #585 | 1 | 2 | yes | — |
| 485 | C8 | — | 2 | 2 | no | — |
| 486 | C8 | — | 2 | 2 | no | — |
| 487 | C8 | — | 2 | 2 | no | — |
| 488 | C8 | — | 4 | 2 | no | — |
| 489 | C8 | — | 4 | 4 | no | — |
| 490 | C8 | — | 4 | 2 | no | — |
| 491 | C8 | C2×#124 | 1 | 2 | yes | — |
| 492 | C8 | C2×#124 | 1 | 2 | yes | — |
| 493 | C22 | — | 2 | 2 | no | — |
| 494 | C22 | — | 2 | 4 | no | — |
| 495 | C22 | — | 4 | 4 | no | — |
| 496 | C22 | — | 4 | 2 | no | — |
| 497 | C22 | — | 4 | 4 | no | — |
| 498 | C22 | — | 8 | 4 | no | — |
| 499 | C22 | — | 8 | 8 | no | — |
| 500 | C22 | — | 16 | 8 | no | — |
| 501 | C22 | — | 32 | 8 | no | — |
| 502 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 503 | C22 | #3514 | 1 | 2 | yes | — |
| 504 | C4 | — | 2 | 4 | no | — |
| 505 | C4 | — | 2 | 2 | no | — |
| 506 | C4 | — | 2 | 2 | no | — |
| 507 | C4 | — | 4 | 2 | no | — |
| 508 | C4 | — | 4 | 4 | no | — |
| 509 | C4 | — | 4 | 2 | no | — |
| 510 | C4 | — | 4 | 2 | no | — |
| 511 | C4 | — | 8 | 2 | no | — |
| 512 | C4 | — | 8 | 4 | no | — |
| 513 | C4 | C22×#124 | 1 | 1 | yes | characteristic |
| 514 | C4 | D4×#41 | 1 | 2 | yes | — |
| 515 | C4 | #3500 | 1 | 1 | yes | characteristic |
| 516 | C2 | — | 2 | 2 | no | — |
| 517 | C2 | — | 4 | 4 | no | — |
| 518 | C2 | — | 8 | 2 | no | — |
| 519 | C2 | — | 16 | 4 | no | — |
| 520 | C2 | D4×#124 | 1 | 1 | yes | characteristic |
| 521 | C2 | #61106 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| prime radical | #61089 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61376 | C2 | semidirect |
| 3. #60626 | C2 | semidirect |
| 4. #33248 | C2 | semidirect |
| 5. #33064 | C2 | semidirect |
| 6. #28763 | C2 | semidirect |
| 7. #28734 | C2 | semidirect |
| 8. #27809 | C2 | semidirect |
| 9. #27292 | C2 | semidirect |
| 10. #25928 | C2 | semidirect |
| 11. #25878 | C2 | semidirect |
| 12. #22466 | C2 | semidirect |
| 13. #21661 | C2 | semidirect |
| 14. #20514 | C2 | semidirect |
| 16. #3504 | C22 | semidirect |
| 24. #3164 | C22 | semidirect |
| 25. C2×#499 | C22 | semidirect |
| 30. #3138 | C22 | semidirect |
| 32. #3136 | C22 | semidirect |
| 36. C2×#490 | C22 | semidirect |
| 37. #3084 | C22 | semidirect |
| 38. #3080 | C22 | semidirect |
| 42. #2960 | C22 | semidirect |
| 47. #2897 | C22 | semidirect |
| 48. #2875 | C22 | semidirect |
| 49. #2641 | C22 | semidirect |
| 50. #2079 | C22 | semidirect |
| 51. #2045 | C22 | semidirect |
| 52. #2037 | C22 | semidirect |
| 53. #2027 | C22 | semidirect |
| 54. #1998 | C22 | semidirect |
| 55. #1995 | C22 | semidirect |
| 56. #1978 | C22 | semidirect |
| 57. #1972 | C22 | semidirect |
| 58. #1970 | C22 | semidirect |
| 59. #1965 | C22 | semidirect |
| 61. #1938 | C22 | semidirect |
| 62. #1931 | C22 | semidirect |
| 63. #1907 | C22 | semidirect |
| 64. #1883 | C22 | semidirect |
| 65. #1838 | C22 | semidirect |
| 66. #1816 | C22 | semidirect |
| 67. #1792 | C22 | semidirect |
| 68. C4×#108 | C22 | semidirect |
| 69. #1772 | C22 | semidirect |
| 70. #1765 | C22 | semidirect |
| 71. #1764 | C22 | semidirect |
| 72. #1759 | C22 | semidirect |
| 73. #1726 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61376 | 2 |
| #61089 | 2 |
| #60626 | 2 |
| #33248 | 2 |
| #33064 | 2 |
| #28763 | 2 |
| #28734 | 2 |
| #27809 | 2 |
| #27292 | 2 |
| #25928 | 2 |
| #25878 | 2 |
| #22466 | 2 |
| #21661 | 2 |
| #20514 | 2 |